heat exchanger design

This illustrates the system calculations involved in selecting a closed feed-water heater, mechanical engineering textbook (Ohio State University). No effort is made to achieve an economic balance between operational costs and the initial investment. The solution focuses primarily on the heat-transfer principles involved and incremental design of size combinations. (We Added some corrections and automated way of calculations)

Principles of Heat Transfer p.181, Introduction to Heat Transfer by Aubrey I. Brown, Salvatore M. Marco, 2nd Edition, McGraw-Hill Book Company Inc.

Problem definition

It is desired to select a closed-type feed-water heater to serve a 100-hp boiler. The boiler operates at 125 psi gauge pressure and delivers steam containing 1 per cent moisture. The heater is to be capable of heating enough water to permit the boiler to operate at 200 percent of its rating. The water is to be heated from 50 to 180F and the necessary heat is to be furnished by saturated steam at 230F. Because of space limitations a vertical type heater not over 10 ft high must be selected. Design the shell and tube heater.

Saturated Liquid @ 139.7 psia

Saturated Vapor @ 139.7 psia

In a typical closed-type feed-water heater, the steam enters on the shell side, while the feed water flows through the tubes.

Condensation of steam: The steam condenses as it gives off its latent heat to the cooler feed water in the tubes. The shell side allows for a larger volume to accommodate the steam's condensation process.

Condensate drainage: The condensate (saturated liquid) that forms after the steam releases its heat can easily be drained from the bottom of the shell.

Tube-side pressure: Water is generally pumped through the tubes because the pressure of feed water is typically higher than that of the steam. Tubes are better suited for handling higher pressure fluids, while the shell side can handle the lower-pressure steam.

The statement that the "boiler operates at 125 psig and delivers steam containing 1 percent moisture" is relevant to understanding the quality and energy content of the steam coming from the boiler, which could affect the overall energy available for heating the water. However, for the specific case of designing the feed-water heater, this detail has minimal impact because the steam being used in the feed-water heater is at a different pressure and temperature (230°F).

Relevance of 1% Moisture in Boiler Steam:

Boiler steam quality: Steam with 1 percent moisture means that the steam is 99 percent dry (or has a steam quality of 99%). This means that not all the steam is in the vapor phase—1% is water droplets. Steam quality impacts the enthalpy (energy content) of the steam.

If we have steam at 125 psig (which corresponds to a saturation temperature of about 353°F), the enthalpy of dry saturated steam (100% dry) is about 1193.2 Btu/lb. But with 1% moisture, the enthalpy is slightly lower:

hactual = hg × Quality = 1193.2 × 0.99 = 1181.3 Btu/lb

So, the steam has slightly less energy compared to 100% dry steam, but this difference is small.

Impact on the Feed-Water Heater Design:

Feed-water heater design: The feed-water heater is receiving steam at 230°F (about 8.8 psig). This steam will either come from a separate extraction point or be reduced in pressure via a valve. The energy content of the steam used for heating the feed water is primarily determined by the 230°F saturation temperature and pressure, not the original 125 psig, 99% dry steam from the boiler.

The 1% moisture mainly affects the overall energy balance of the boiler and its ability to meet steam demands, but it does not have a direct, significant impact on the specific heat transfer calculations for the feed-water heater.

While the 1% moisture slightly reduces the energy content of the steam being generated by the boiler, its impact on the feed-water heater design is negligible (1%) since the steam for the heater is at a different pressure and temperature (230°F). The focus for the feed-water heater design remains on the heat transfer requirements using the specified 230°F saturated steam. However, in our case, we will include the 1% when computing for enthalpy of wet steam.

Table for the initial boundary conditions using Logarithmic Mean Temperature Difference (LMTD) at 101.5F.

SOLUTION

1. Boiler System:

The boiler takes water preheated by the feedwater heater and converts it into steam.

Boiler Inputs:

Feedwater temperature: 180°F (after preheating in the feedwater heater).
Boiler operating pressure: 125 psig = 139.7 psia.
Steam quality: 99% vapor, 1% moisture (vapor fraction, x = 0.99).
Boiler heat output: 200% of rated capacity = 6,695,000 Btu/hr.

Enthalpy of Steam with 1% Moisture at 139.7 psia:

Enthalpy of saturated liquid (hf): 324.76 Btu/lb.
Enthalpy of saturated vapor (hg): 1194.2 Btu/lb.
Latent heat (hfg = hg − hf): 869.44 Btu/lb.

Given the 1% moisture, the steam's enthalpy is:

hwet-steam= hf + x⋅hfg = 324.76 + 0.99⋅869.44 =324.76 + 860.75 = 1185.51 Btu/lb.

Heat Added in the Boiler:

The water enters the boiler at 180°F and is converted to steam. We need to calculate the heat added to turn the feedwater into steam.

Enthalpy of water at 180°F (approx): 148 Btu/lb.
Heat added per lb of water:

Qadded = hwet-steam−hwater =1185.51 Btu/lb − 148 Btu/lb = 1037.51 Btu/lb

Mass Flow Rate of Steam:

Boiler heat output: 6,695,000 Btu/hr (200% of the rated capacity @ 100HP).
Heat added per lb of steam: 1037.51 Btu/lb.

msteam = 6,695,000 Btu/hr / 1037.51 Btu/lb ≈ 6454 lb/hr.

2. Feedwater Heater System:

The feedwater heater preheats the water before it enters the boiler.

Feedwater Heater Inputs:

Inlet water temperature: 50°F.
Outlet water temperature: 180°F (enters the boiler at this temperature).
Specific heat of water (Cp): 1 Btu/lb°F.

Heat Transfer in the Feedwater Heater:

The heat added to the water in the feedwater heater is:

Qfeedwater = m⋅Cp⋅ΔT.

ΔT = Tfinal - Tinitial = 180°F - 50°F = 130°F.
Mass flow rate: The same as the steam mass flow rate, 6454 lb/hr (since the same amount of water that enters the boiler as feedwater will eventually be converted to steam).

Qfeedwater = 6454 lb/hr × 1 Btu/lb°F × 130 °F = 838,520 Btu/hr.

INITIAL ITERATION:

theory of the shell/tube side

In a shell-and-tube heat exchanger, particularly when using steam on the shell side to heat water on the tube side, it's quite common for the inlet and outlet temperatures of the steam to remain the same. This happens because of the process of condensation.

Here's why the shell side (steam) inlet and outlet temperatures are the same in this scenario:

Saturated Steam at Constant Temperature:

When steam is in a saturated state, it means that it's at the boiling point for its pressure (in this case, 230°F at 139.7 psia). As long as the steam is condensing (changing from vapor to liquid), it will remain at this same temperature. This is because phase changes (like boiling or condensing) occur at constant temperature when pressure is constant.

The latent heat of vaporization is released during the phase change, but this does not affect the temperature of the steam. So, as steam condenses to water, it releases heat, but its temperature remains constant.

Condensation in Heat Exchanger:

In the heat exchanger, the steam enters at 230°F and starts to condense as it gives up its latent heat to the cooler feedwater on the tube side. As it condenses, it remains at 230°F until it has completely turned into liquid.

By the time the steam exits the heat exchanger, it's mostly liquid water at 230°F (with possibly some subcooling, but usually minimal). Thus, the temperature of the steam does not change during the heat transfer process.

Latent Heat Transfer:

The majority of the heat transfer in this type of heat exchanger comes from the latent heat of vaporization (the energy required to change the steam from vapor to liquid). Even though the steam is giving up a lot of energy (in this case, 869.44 Btu/lb), it stays at the same temperature because it’s a phase change process.

Once the steam is fully condensed, further cooling would result in a temperature drop, but that typically doesn't happen in this context, where the goal is to heat the feedwater efficiently.

THE HEAT TRANSFER:

The tube side (feedwater) sees a significant temperature change (from 50°F to 180°F), while the shell side (steam) temperature remains constant because the steam is condensing. The heat transferred from the steam to the water is due to the latent heat released by the steam as it condenses, not due to a temperature difference in the steam itself.

The constant temperature of the steam ensures a high and consistent heat transfer rate, which is ideal for preheating the feedwater.

Pointers:

Steam temperature stays the same during condensation at constant pressure.

Latent heat is what drives the heat transfer.

Feedwater temperature increases, while steam temperature does not drop during condensation.

This is a very efficient way to use steam in heat exchangers, as it maximizes the energy transfer without needing a large temperature difference on the steam side.

final iteration

shell side monitor

tube side monitor

vibration

api 660 spec sheet

rating data sheet

tema spec sheet

property monitor

stream properties

GEOMETRY sketch

summary:

After simulating various parameters to meet the specified boundary conditions for the design of the heat exchanger, it was determined that the limiting height of 10 ft for the vertical heat exchanger is NOT feasible. Although, in theory, the desired vertical heat exchanger can achieve the necessary performance, it cannot be constructed according to the current engineering standards, such as API 660 and TEMA (Tubular Exchanger Manufacturers Association) ratings.

These standards impose strict requirements on heat exchanger dimensions, materials, and safety factors, which the design cannot satisfy while maintaining a height under 10 feet. Therefore, modifications to the design or a different type of heat exchanger would be required to meet both performance and construction standards.

Based on the current standards and constructibility requirements, the minimum height that meets all specifications and practical considerations is 12 feet, 3 and 3/8 inches. This accounts for factors like mechanical design, material limits, and space constraints, ensuring the unit is compliant with industry standards. Q. E. D.

design without height constraint

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